On the diophantine equation $\bigl(\frac{x}{y}\bigr)^u+\bigl(\frac{y}{z}\bigr)^v+\bigl(\frac{z}{x}\bigr)^w=4t$

M. Z. Garaev

Geodesic

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On the diophantine equation $\bigl(\frac{x}{y}\bigr)^u+\bigl(\frac{y}{z}\bigr)^v+\bigl(\frac{z}{x}\bigr)^w=4t$

M. Z. Garaev

Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 1, pp. 267-270.

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Résumé

It is proved that the equation $\bigl(\frac{x}{y}\bigr)^u+\bigl(\frac{y}{z}\bigr)^v+\left(\frac{z}{x}\right)^w=4t$ has no solutions in positive integers $x,y,z,t,u,v,w$.

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@article{FPM_2001_7_1_a14,
     author = {M. Z. Garaev},
     title = {On the diophantine equation $\bigl(\frac{x}{y}\bigr)^u+\bigl(\frac{y}{z}\bigr)^v+\bigl(\frac{z}{x}\bigr)^w=4t$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {267--270},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a14/}
}

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M. Z. Garaev. On the diophantine equation $\bigl(\frac{x}{y}\bigr)^u+\bigl(\frac{y}{z}\bigr)^v+\bigl(\frac{z}{x}\bigr)^w=4t$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 1, pp. 267-270. http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a14/